Sitting in a corner by the bar at 34, the new restaurant from the group behind the Ivy and Le Caprice among others, is a box-fresh baby grand piano. I'll be honest – that's enough for me. Any restaurant can invest in new cruet sets, a serious steak grill – the must-have accessory in London's high-end kitchens these days – or enough crisp linen to wrap the Reichstag. But spending a fat four-figure sum on a beautiful hunk of wood and wire shows an uncommon commitment. As an enthusiastic (as against good) jazz pianist, it thrills me they have decided to install someone at the keys every night; indeed, that there will be a jazz trio on Thursdays, Fridays and Saturdays. It is a romantic, classy, gloriously old-fashioned touch.

All of which sums up the place. 34 is the most self-assured, delicious London restaurant launch in years. Everything, from the look of the place through the killer steaks to the desserts, is bang on. It is sexy and smart. Most of all it feels like it has been there for years rather than just a few weeks.

At which point I should declare an interest: I am a member of the Ivy Club, which is also owned by the perennially young Richard Caring, boss of the group that owns 34. This, however, has never stopped me saying what I think about his other places; Google my recent review of Le Caprice, then wash the blood off your hands. It did mean that I didn't have trouble getting a table at a reasonable hour, when they were otherwise offering high tea or bed time. Amusingly they asked me not to mention this in the review because they didn't want to give the impression that it's just a place for those in the know. For the owners of the Ivy to worry about people thinking they are just for VIPs is a little like a lion getting upset for being called a carnivore. And, anyway, it's part of the appeal. One of the reasons for wanting to eat at these restaurants is the allure of the phone-hackerati who are said to eat there. On any given night many tables really are filled by those whose privacy the tabs have deemed worth invading.

34 will soon be the same, and yet with a bit of planning getting a table at a sensible time is doable. The food is worth the effort. Witness a soft onion tart of flaky, buttery pastry with perfectly sautéed lamb sweetbreads and a slick of sweet-savoury jus, or a plate of salt-baked beets with a tumble of burrata, the in-vitro version of mozzarella.

In early publicity, 34 allowed itself to be billed as a meaty version of its sister fish restaurant Scott's. I'm not sure that's true. The menu is broader than that. But certainly a list of very good steaks is at its core, including Australian Wagyu at fearsome prices and Scottish cuts which are both more affordable and leave less of a whacking carbon footprint, with American steaks in between. My rib eye was simply a great piece of meat, cooked with care and precision. We loved another dish of long-braised short rib, slipping from the bone, with winter vegetables. Sides are worth making space for: creamed sweet corn with chilli and basil or Brussels sprouts with a crust of crumbed prosciutto and hazelnuts.

And then there's dessert. In a city where you can have anything you like as long as it's a chocolate fondant, a crème brûlée or a lemon tart, the 34 list is special. We didn't have the pear tart or the sloe-gin fizz jelly or the butterscotch sponge pudding. We did have the chocolate bomb, a sphere of chocolate on to which was poured a hot sauce of same, melting it to reveal mint ice cream. There were also hot, sugared donuts with a dipping bowl of a zingy lemon curd and another of chocolate sauce. And if you don't want to eat that right this instant, you are reading the wrong page.

Is any of this cheap? Don't be silly. This is a flash restaurant in the flashiest corner of flash London. But with cold, economic winds blowing hard in 2012, we need to know where it's worth spending whatever spare cash we might have. 34 is that place.